In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message. The formula for entropy was introduced by Claude E. Shannon in his paper "A Mathematical Theory of Communication".
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Expression is also called an uncertainty or surprisal, the lower the probability , i. Cormack, Bogdan Filipic, Thomas R. The most significant difference lies in the types of state-transitions allowed in each sort of model. This difference does not correspond to the difference that would be expected after considering the ordinary usage of these terms. Buhmann, "Information theoretic model validation for clustering", arxiv Burnham and David R.
Charalambous, Photios A. Chaves, L. Luft, T. Maciel, D. Gross, D.
Janzing, B. Chen and T. Ciuperca, V.
Girardin and L. Dembo and I. Drmota and W. Ultimately, the efficiency measure can be directly interpreted as the relative entropy between two probability distributions, namely: the distribution of the particles in the presence of the external rectifying force field and a reference distribution describing the behavior in the absence of the rectifier".
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Interesting for the link between relative entropy and energetics. Follmer, "On entropy and information gain in random fields", Z. Godavarti and A. Gorban, Iliya V. Greven, G.
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Keller and G. Warnecke eds. Our fundamental philosophy in doing so is first to convert all of the hypothesis testing problems completely to the pertinent computation problems in the large deviation-probability theory.
Such general formulas are presented from the information-spectrum point of view. Haydn, "The Central Limit Theorem for uniformly strong mixing measures", arxiv He and E. Mees, "Estimating topological entropy via a symbolic data compression technique," Physical Review E 67 : S. Ho and S. Ho and R. Hotta and I.
Iwata, K. Ikeada and H. Kennel, "Testing time symmetry in time series using data compression dictionaries", Physical Review E 69 : D. Kieffer and E. Principe, "Vector quantization using information theoretic concepts", Natural Computation 4 : F. Liang and A.
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Broomhead, Joshua Knowles, Marcelo A. Montemurro, Douglas B. Kell, "Information-theoretic sensitivity analysis: a general method for credit assignment in complex networks", Journal of the Royal Society: Interface forthcoming E. Lutwak, D. Yang and G. Majda, Rafail V.
Information entropy (video) | Khan Academy
Abramov and Marcus J. Merhav and M. Meron and M. Mitter and Nigel J. Newton, "Information and Entropy Flow in the Kalman-Bucy Filter", Journal of Statistical Physics : [This looks rather strange, from the abstract, but potentially interesting Duhamel, "Geometrical interpretation and improvements of the Blahut-Arimoto's algorithm", arxiv Entropy, 20 9. Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets.
All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level.